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Method for storage and reconstruction of the extended hamming code for an 8-dimensional lattice quantizer

  • US 6,404,820 B1
  • Filed: 07/09/1999
  • Issued: 06/11/2002
  • Est. Priority Date: 07/09/1999
  • Status: Expired due to Term
First Claim
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1. A method of lattice-quantizing an eight-long data point in a manner that minimizes storage requirements, comprising the steps of:

  • a) acquiring the eight-long data point;

    b) multiplying each coordinate of the data point by the square root of two to form an inflated data point;

    c) rounding each coordinate of the inflated data point to the nearest integer;

    d) modulo-two reducing each coordinate of the rounded inflated data point to form an initial codeword;

    e) creating a signal packet, wherein said step of creating a signal packet is comprised of the steps of;

    constructing a signal packet, if the initial codeword is an all-0s codeword in shell 1, having four bits set to an all-0s code, having one bit to indicate that the rounded and inflated data point is in shell 1, having three bits to indicate which bit in the rounded and inflated data point must be changed to a 2, and having one bit to indicate the polarity of the 2;

    constructing a signal packet, if the initial codeword is an all-0s codeword in shell 2, having four bits set to an all-0s code, having one bit to indicate that the rounded and inflated data point is in shell 2, having five bits to indicate the position in a table where the locations in the rounded and inflated data point that must be changed to 2 can be found;

    having one bit to indicate the polarity of the first 2; and

    having one bit to indicate the polarity of the second 2;

    constructing a signal packet, if the initial codeword is an all-1s codeword in shell 2, having four bits set to an all-1s code, having one bit to indicate the polarity of a first 1 in the rounded and inflated data point, having one bit to indicate the polarity of a second 1 in the rounded and inflated data point, having one bit to indicate the polarity of a third 1 in the rounded and inflated data point, having one bit to indicate the polarity of a fourth 1 in the rounded and inflated data point, having one bit to indicate the polarity of a fifth 1 in the rounded and inflated data point, having one bit to indicate the polarity of a sixth 1 in the rounded and inflated data point, having one bit to indicate the polarity of a seventh 1 in the rounded and inflated data point, and having one bit to indicate the polarity of an eighth 1 in the rounded and inflated data point;

    constructing a signal packet, if the initial codeword is a weight-four codeword in shell 1, having four bits set to indicate an extended quadratic residue code codeword from which an Extended Hamming Code codeword may be calculated, having one bit to indicate that the rounded and inflated data point is in shell 1, having one bit to indicate the polarity of a first 1 in the rounded and inflated data point, having one bit to indicate the polarity of a second 1 in the rounded and inflated data point, having one bit to indicate the polarity of a third 1 in the rounded and inflated data point, and having one bit to indicate the polarity of a fourth 1 in the rounded and inflated data point;

    constructing a signal packet, if the initial codeword is a weight-four codeword in shell 2, having four bits set to indicate an extended quadratic residue code codeword from which an Extended Hamming Code codeword may be calculated, having one bit to indicate that the rounded and inflated data point is in shell 2, having one bit to indicate the polarity of a first 1 in the rounded and inflated data point, having one bit to indicate the polarity of a second 1 in the rounded and inflated data point, having one bit to indicate the polarity of a third 1 in the rounded and inflated data point, and having one bit to indicate the polarity of a fourth 1 in the rounded and inflated data point, having two bits to indicate which 0 in the rounded and inflated data point must be changed to a 2, and having one bit to indicate the polarity of the 2; and

    f) transmitting the signal packet to a receiver.

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